Geodesic
The spectral sequence of a~fibration and the skeletons of the base
Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 173-183

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An analog is constructed of the spectral sequence for a fibration given over some skeleton of a cellular space. The construction is applied to construct an isomorphism of the first k terms of the spectral sequences of two fibrations with common cellular base whose restrictions to the $(k-1)$-skeleton of the base coincide. 
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     author = {V. V. Rokhlin},
     title = {The spectral sequence of a~fibration and the skeletons of the base},
     journal = {Matemati\v{c}eskie zametki},
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V. V. Rokhlin. The spectral sequence of a~fibration and the skeletons of the base. Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 173-183. http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a18/